If `sum_(r=0)^n{a_r(x-alpha+2)^r-b_r(alpha-x-1)^r}=0,` then prove that `b_n-(-1)^n a_n=0.`

If sum_(r=0)^(2n)a_r(x-2)^r=sum_(r=0)^(2n)b_r(x-3)^ra n da_k=1 for all kgeqn , then show that b_n=^(2n+1)C_(n+1) .

If (1-x^2)^n=sum_(r=0)^n a_r x^r(1-x)^(2n-r),t h e na_r is equal to a.) ^n C_r b.) ^nC_r3^r c.) ^2n C_r d.) ^nC_r2^r

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

The value of sum_(r=0)^(3n-1)(-1)^r 6nC_(2r+1)3^r is

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to

If sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64) where n, p in N , then

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a= (^n C_2)^2 b. ^n C_rdot^n C_(r+1) c. ^2n C_r d. ^2n C_(r+1)

If sum_(r=0)^nr/(^n C_r)=sum_(r=0)^n(n^2-3n+3)/(2.^n C_r) , then a. n=1 b. n=2 c. n=3 d. none of these

If sum_(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+r)=(675)/(26) , then n equal to

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.